abstract in this paper, we study the generalized order- jacobsthal sequences modulo for and the generalized order-k jacobsthal-padovan sequence modulo for . also, we define the generalized order-k jacobsthal orbit of a k-generator group for and the generalized order-k jacobsthal-padovan orbit a k-generator group for . furthermore, we obtain the lengths of the periods of the generalized order-3 ...

Abstract In this paper, we study the generalized order- Jacobsthal sequences modulo for and the generalized order-k Jacobsthal-Padovan sequence modulo for . Also, we define the generalized order-k Jacobsthal orbit of a k-generator group for and the generalized order-k Jacobsthal-Padovan orbit a k-generator group for . Furthermore, we obtain the lengths of the periods of the generalized order-3 ...

In this paper we present the sequence of the k-Jacobsthal-Lucas numbers that generalizes the Jacobsthal-Lucas sequence introduced by Horadam in 1988. For this new sequence we establish an explicit formula for the term of order n, the well-known Binet’s formula, Catalan’s and d’Ocagne’s Identities and a generating function. Mathematics Subject Classification 2010: 11B37, 11B83

In this paper we present new families of sequences that generalize the Jacobsthal and the Jacobsthal-Lucas numbers and establish some identities. We also give a generating function for a particular case of the sequences presented. Introduction Several sequences of positive integers were and still are object of study for many researchers. Examples of these sequences are the well known Fibonacci ...

S. Magliveras and W. Wei∗, Florida Atlantic University Let Σ = {0, 1} be the binary alphabet, and A = {0, 01, 11} the set of three strings 0, 01, 11 over Σ. Let A∗ denote the Kleene closure of A, and Z the set of positive integers. A sequence in A∗ is called a Jacobsthal binary sequence. The number of Jacobsthal binary sequences of length n ∈ Z is the n Jacobsthal number. Let k ∈ Z, 1 ≤ k ≤ n. ...

We show how to apply the Collatz function and the modified Collatz function to the ternary representation of a positive integer, and we present the ternary modified Collatz sequence starting with a multiple of 3N for an arbitrary large integer N . Each ternary string in the sequence is shown to have a repeating string, and the number of occurrences of each digit in each repeating string is iden...

In this study, we define the hyperbolic Jacobsthal-Lucas numbers and obtain recurrence relations, Binet’s formula, generating function summation formulas for these numbers.

This paper, in considering aspects of the geometric mean sequence, offers new results connecting Jacobsthal and Horadam numbers which are established and then proved independently.

In this paper, one of the special integer sequences, Jacobsthal and Lucas sequences which are encountered in computer science is generalized according to parity index entries called bi-periodic sequences. The definitions given by using classic literature, there were some relations for We find new identities these If we substitute a=b=1 results, get